Lottery Game Design White PapersPrev TopicNext Topic

• lucky1day

  

  South Holland
  United States
  Member #178,682
  December 11, 2016
  250 Posts
  Offline
  Jan 17, 2017, 6:09 pm

  ▲▼

  Hello Everyone,

  Long time lurker, first time poster obviously.

  I was hoping that someone could point me in the direction for information on how lottery games are designed in terms of payout structure. White papers or any other information would be great.

  Here is an example structure using power ball (white balls only):

  Total combinations: 11,238,513

  Match 5: 1

  Match 4: 320

  Match 3: 20,160

  Match 2: 416,640

  Match 1 or 0: 10,801,392

  I hope this is posted in the correct forum

  Thanks in advance.

  Lucky1day
• RJOh

  

  100

  mid-Ohio
  United States
  Member #9
  March 24, 2001
  20,272 Posts
  Offline
  Jan 18, 2017, 4:20 pm

  ▲▼

  One thing I know is the payouts are about 50% of sales so the states make a profit.  If you calculate all the possible winners and multiply them by their payout amounts, their total amount will be about 50% of the amount to purchase all the possible combinations.

   * you don't need to buy every combination, just the winning ones * 

         
  
• RJOh

  

  100

  mid-Ohio
  United States
  Member #9
  March 24, 2001
  20,272 Posts
  Offline
  Jan 18, 2017, 7:55 pm

  ▲▼

  I did as I suggested in my previous post for games I've played when their jackpots are their lowest amount with cash option.
  
  Buying all 258890850 MegaMillons combinations would cost $258,890,850.00 and payout $54,856,964.00 or 21% of sales.
  Buying all 292201338 PowerBall combinations would cost $548,402,676.00 and payout $119,466.048.00 or 20% of sales.
  Buying all 13983816 Ohio's Classic Lotto(6/49) combinations would cost $13,983,816.00 and payout $2,328,790.00 or 16% of sales.
  Buying all 575757 RollingCash5(5/39) combinations would cost $575,757.00 and payout $266,940.00 or 46% of sales.
  
  Inspite of my calculations, lottery websites claim 50% of sales goes for *payouts.
  * payouts would be higher with larger jackpot amounts, for example if Rolling Cash5 jackpot exceed $408,817.00, payout would equal or exceed cost of tickets.

   * you don't need to buy every combination, just the winning ones * 

         
  
• JADELottery

  

  Eagle Sun

  IA, MN, WI
  United States
  Member #21
  December 7, 2001
  5,177 Posts
  Offline
  Jan 19, 2017, 8:36 am

  ▲▼

  One White Paper on payouts is:

  

   

  But all kidding aside, there is a way to measure payouts to odds.

  It's by the Odd / Dollar.

  Or, Odds per payout Dollar, Odds / $Payout.

  As an example, if we take the Pick 3 Straight payout of $500.00 and divide it into its odds of 1 in 1,000, we use 1,000 / $500.00 and get 2 Odd / Dollars.

  The lower the Odd / Dollar, the better the payout.

  Sticking with Pick 3, a 6-way Box pays out $80.00 and the Odds are 1 in 167, divide 167 by $80.00 we get 2.0875.

  It's a little less better than a Pick 3 Straight, but not much.

  Now, let's look at Powerball and Mega Millions; just the fixed basic payouts, not the jackpot, Power Play or Megaplier.

  With Powerball, there is one more thing to factor in, the Play cost.

  Since Powerball cost $2.00, we have to multiply the Odd / Dollar by 2.00 to get the final Odd / Dollar value.

  It's because it takes twice as much monetary power on part of the player to achieve a win.

  Below is a table of the Payouts, Odds and Odd / Dollars for each game and factored by their Play cost.

  Keep in mind, the lower the Odd / Dollar the better the Payout.

  Powerball
  Win	Payout	Odds	Odd / Dollar
  0 + 1	$4.00	38.00	19.0000
  1 + 1	$4.00	92.00	46.0000
  2 + 1	$7.00	701.00	200.2857
  3 + 1	$100.00	14494.00	289.8800
  4 + 1	$50,000.00	913129.00	36.5252
  3 + 0	$7.00	580.00	165.7143
  4 + 0	$100.00	36525.00	730.5000
  5 + 0	$1,000,000.00	11688054.00	23.3761

   

  Mega Millions
  Win	Payout	Odds	Odd / Dollar
  0 + 1	$1.00	21.39	21.3900
  1 + 1	$2.00	56.47	28.2350
  2 + 1	$5.00	472.95	94.5900
  3 + 1	$50.00	10720.12	214.4024
  4 + 1	$5,000.00	739688.14	147.9376
  3 + 0	$5.00	765.72	153.1440
  4 + 0	$500.00	52834.87	105.6697
  5 + 0	$1,000,000.00	18492203.57	18.4922

  The One Over None
  I Know...
• JADELottery

  

  Eagle Sun

  IA, MN, WI
  United States
  Member #21
  December 7, 2001
  5,177 Posts
  Offline
  Jan 19, 2017, 8:58 am

  ▲▼

  As you can see, the worst payout between the two is Powerball's 4 + 0 of just a $100.00.

  Compared to Mega Millions' 4 + 0 of $500.00, Mega Millions has the better payout.

  In both, the 3 + 1 is a poor payout.

  What we've seen in the past is about a 10 Odd / Dollar or less as being a relatively good payout.

  Anything above 10 Odd / Dollars is considered a poor payout, in our opinion.

  The One Over None
  I Know...
• lucky1day

  

  South Holland
  United States
  Member #178,682
  December 11, 2016
  250 Posts
  Offline
  Jan 19, 2017, 9:10 am

  ▲▼

  Hi Guys,

   

  Thanks for the replies, but I'm actually interested in how the tiers were design. There is obviously a mathematical relationship that keeps the game unbalanced toward the ticket buyer. If you look at the white ball structure for power ball, you will noticed that there are 10,801,392 tickets that could never win with a given combination. That leaves approximately 437,121 prizes. This balance has to be derived from some mathematical expression that is what I'm after.

  Thanks again for your replies.

   

  Lucky1day
• JADELottery

  

  Eagle Sun

  IA, MN, WI
  United States
  Member #21
  December 7, 2001
  5,177 Posts
  Offline
  Jan 19, 2017, 11:31 am

  ▲▼
  In response to lucky1day

  Quote: Originally posted by lucky1day on Jan 19, 2017

  Hi Guys,

   

  Thanks for the replies, but I'm actually interested in how the tiers were design. There is obviously a mathematical relationship that keeps the game unbalanced toward the ticket buyer. If you look at the white ball structure for power ball, you will noticed that there are 10,801,392 tickets that could never win with a given combination. That leaves approximately 437,121 prizes. This balance has to be derived from some mathematical expression that is what I'm after.

  Thanks again for your replies.

   

  Lucky1day

  what you are looking for might more on the financial part of the lottery, because that's what is going to determine payout structures.

  however, from the player's perspective, the best we could do is to reverse engineer the process using the available information about payouts and odds.

  hence, the Odd / Dollar; it a start, but needs further work.

  The One Over None
  I Know...
• JADELottery

  

  Eagle Sun

  IA, MN, WI
  United States
  Member #21
  December 7, 2001
  5,177 Posts
  Offline
  Jan 19, 2017, 12:20 pm

  ▲▼

  If the big ones would like a suggestion.

  This would definitely juice things up.

  But like we said, it's just a suggestion; multipliers aside of course.

  We think the players would be pleased.

   

  Powerball
  Win	Actual	Suggested
  0 + 1	$4.00	$8.00
  1 + 1	$4.00	$18.00
  2 + 1	$7.00	$140.00
  3 + 1	$100.00	$2,800.00
  4 + 1	$50,000.00	$180,000.00
  3 + 0	$7.00	$110.00
  4 + 0	$100.00	$7,000.00
  5 + 0	$1,000,000.00	$2,000,000.00

   

   

  Mega Millions
  Win	Actual	Suggested
  0 + 1	$1.00	$2.00
  1 + 1	$2.00	$6.00
  2 + 1	$5.00	$45.00
  3 + 1	$50.00	$1,000.00
  4 + 1	$5,000.00	$70,000.00
  3 + 0	$5.00	$75.00
  4 + 0	$500.00	$5,000.00
  5 + 0	$1,000,000.00	$1,500,000.00

  The One Over None
  I Know...
• Sunglasses

  Belgium
  Member #173,922
  March 26, 2016
  1,396 Posts
  Offline
  Jan 19, 2017, 3:14 pm

  ▲▼
  In response to lucky1day

  Quote: Originally posted by lucky1day on Jan 19, 2017

  Hi Guys,

   

  Thanks for the replies, but I'm actually interested in how the tiers were design. There is obviously a mathematical relationship that keeps the game unbalanced toward the ticket buyer. If you look at the white ball structure for power ball, you will noticed that there are 10,801,392 tickets that could never win with a given combination. That leaves approximately 437,121 prizes. This balance has to be derived from some mathematical expression that is what I'm after.

  Thanks again for your replies.

   

  Lucky1day

  See above for the simulation. You can simulate playing all like 75 + 15 and winning 5 + 1.

  The payouts depend of what is in the payable pot. Calculations can be improvised, depending of the lottery, there is a meeting to decide what they do with the money. A part of the money is going to schools, sport or other.